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1.
Alcides Buss 《Bulletin of the Brazilian Mathematical Society》2010,41(4):607-641
We study integrability for coactions of locally compact groups. For abelian groups, this corresponds to integrability of the
associated action of the Pontrjagin dual group. The theory of integrable group actions has been previously studied by Ruy
Exel, Ralf Meyer and Marc Rieffel. Our goal is to study the close relationship between integrable group coactions and Fell
bundles. As a main result, we prove that dual coactions on C*-algebras of Fell bundles are integrable, generalizing results by Ruy Exel for abelian groups. 相似文献
2.
Astrid an Huef 《Journal of Functional Analysis》2011,260(5):1543-1581
We generalise the Dixmier-Douady classification of continuous-trace C?-algebras to Fell algebras. To do so, we show that C?-diagonals in Fell algebras are precisely abelian subalgebras with the extension property, and use this to prove that every Fell algebra is Morita equivalent to one containing a diagonal subalgebra. We then use the machinery of twisted groupoid C?-algebras and equivariant sheaf cohomology to define an analogue of the Dixmier-Douady invariant for Fell algebras, and to prove our classification theorem. 相似文献
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4.
B. Sheppard 《Mathematische Zeitschrift》2004,246(1-2):105-110
We prove that the Stone-Weierstrass conjectures for C*-algebras and JB*-algebras are equivalent. 相似文献
5.
Ruy Exel 《Mathematische Annalen》2002,323(2):259-266
Kirchberg and Wasserman's Theorem, according to which a group is exact if and only if its reduced C*-algebra is exact, is
extended to the context of Fell bundles.
Received: 31 December 2000 / Revised version: 7 August 2001 / Published online: 4 April 2002 相似文献
6.
Translation algebras of finitely generated *-algebras of bounded linear operators on a separable Hilbert space are introduced. Two equivalent forms of amenability for finitely generated *-algebras in terms of the existence of Følner sequences are introduced. These are related to the existence of traces on the associated translation algebra and, in the context of C*-algebras, are related to weak-filterability and to the existence of hypertraces. 相似文献
7.
Wei Guoqiang 《数学年刊B辑(英文版)》1998,19(4):465-472
1.IntroductionInwhatfollows,allofHilbertspacesappearedinthispaperareinfinite-dimensionalseparablecomplexHilbertspace.IfHisaHilbertspace,thenC(n)denotestheC*--algebraofallboundedlinearoperatorsonHandK(H)denotesthesetofcompactoperatorsonn.TwooperatorsSandTarecalledapproximatelyequivalentifthereisasequenc{Un}ofunitaryoperatorssuchthatlIU:SUn--Tll-0(n-- co).SimilarlytwooperatosSandTareapproximatelysimilarifthereisasequence{Vn}ofinvertibleoperatorswithsup(llVn11,11VJ'11)相似文献
8.
In this paper injective real W*-algebras are investigated. It is shown that injectivity is equivalent to the property of E (extension property). It is proven that a real W*-algebra is injective iff its hermitian part is injective, and it is equivalent to, that the enveloping W*-algebra is also injective. Moreover, it is shown that if the second dual space of a real C*-algebra is injective, then the real C*-algebra is nuclear. 相似文献
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10.
George K. Eleftherakis Evgenios T.A. Kakariadis Elias G. Katsoulis 《Israel Journal of Mathematics》2017,222(2):949-972
We revisit a central result of Muhly and Solel on operator algebras of C*-correspondences. We prove that (possibly non-injective) strongly Morita equivalent C*-correspondences have strongly Morita equivalent relative Cuntz–Pimsner C*-algebras. The same holds for strong Morita equivalence (in the sense of Blecher, Muhly and Paulsen) and strong Δ-equivalence (in the sense of Eleftherakis) for the related tensor algebras. In particular, we obtain stable isomorphism of the operator algebras when the equivalence is given by a σ-TRO. As an application we show that strong Morita equivalence coincides with strong Δ-equivalence for tensor algebras of aperiodic C*-correspondences. 相似文献
11.
Let C be a class of unital C*-algebras. The class TAC of C*-algebras which can be tracially approximated (in the Egorov-like sense first considered by Lin) by the C*-algebras in C is studied (Lin considered the case that C consists of finite-dimensional C*-algebras or the tensor products of such with C([0,1])). In particular, the question is considered whether, for any simple separable A∈TAC, there is a C*-algebra B which is a simple inductive limit of certain basic homogeneous C*-algebras together with C*-algebras in C, such that the Elliott invariant of A is isomorphic to the Elliott invariant of B. An interesting case of this question is answered. In the final part of the paper, the question is also considered which properties of C*-algebras are inherited by tracial approximation. (Results of this kind are obtained which are used in the proof of the main theorem of the paper, and also in the proof of the classification theorem of the second author given in [Z. Niu, A classification of tracially approximately splitting tree algebra, in preparation] and [Z. Niu, A classification of certain tracially approximately subhomogeneous C*-algebras, PhD thesis, University of Toronto, 2005]—which also uses the main result of the present paper.) 相似文献
12.
13.
Edward Kissin 《Journal of Functional Analysis》2006,236(2):609-629
In this paper we consider automorphisms of the domains of closed *-derivations of C*-algebras and show that they extend to automorphisms of C*-algebras, so we call them diffeomorphisms. The diffeomorphisms generate transformations of the sets of closed *-derivations of C*-algebras. In this paper we study the subgroups of diffeomorphisms that define “bounded” shifts of derivations and the subgroups of the stabilizers of derivations. 相似文献
14.
We prove that operator algebras that have enough projections are completely determined by those projections, their symmetries, and the action of the latter on the former. This includes all von Neumann algebras and all AW*-algebras. We introduce active lattices, which are formed from these three ingredients. More generally, we prove that the category of AW*-algebras is equivalent to a full subcategory of active lattices. Crucial ingredients are an equivalence between the category of piecewise AW*-algebras and that of piecewise complete Boolean algebras, and a refinement of the piecewise algebra structure of an AW*-algebra that enables recovering its total structure. 相似文献
15.
We construct a weak conditional expectation from the section C*-algebra of a Fell bundle over a unital inverse semigroup to its unit fibre. We use this to define the reduced C*-algebra of the Fell bundle. We study when the reduced C*-algebra for an inverse semigroup action on a groupoid by partial equivalences coincides with the reduced groupoid C*-algebra of the transformation groupoid, giving both positive results and counterexamples. 相似文献
16.
《Expositiones Mathematicae》2022,40(4):947-960
In this article we show that the main C*-algebras describing the canonical commutation relations of quantum physics, i.e., the Weyl and resolvent algebras, are in the class of Følner C*-algebras, a class of C*-algebras admitting a kind of finite approximations of Følner type. In particular, we show that the tracial states of the resolvent algebra are uniform locally finite dimensional. 相似文献
17.
N. Christopher Phillips 《Israel Journal of Mathematics》2007,160(1):189-217
We give examples of minimal diffeomorphisms of compact connected manifolds which are not topologically orbit equivalent, but
whose transformation group C*-algebras are isomorphic. The examples show that the following properties of a minimal diffeomorphism
are not invariants of the transformation group C*-algebra: having topologically quasidiscrete spectrum; the action on singular
cohomology (when the manifolds are diffeomorphic); the homotopy type of the manifold (when the manifolds have the same dimension);
and the dimension of the manifold.
These examples also give examples of nonconjugate isomorphic Cartan subalgebras, and of nonisomorphic Cartan subalgebras,
of simple separable nuclear unital C*-algebras with tracial rank zero and satisfying the Universal Coefficient Theorem.
The research was partially supported by the NSF grants DMS 9706850, DMS 0070776, DMS 0302401, and by the MSRI. 相似文献
18.
H. Narnhofer 《Journal of Mathematical Sciences》2005,131(2):5538-5546
The C*-algebras associated with irrational rotations are Morita equivalent if and only if the rotation parameters belong to
the same orbit under the action of GL(2, Z). In this note, we suggest explicit type II representations such that the bimodule
is dense in the corresponding Hilbert space. Bibliography: 4 titles.
__________
Published in Zapiski Nauchnykh Seminarov POMI, Vol. 307, 2004, pp. 175–188. 相似文献
19.
共变完全多正线性映射的共变投射表示 总被引:1,自引:0,他引:1
研究了C*-代数中的共变完全多正线性映射,证明了共变完全多正线性映射可以诱导Hilbert C*-模上的共变投射表示,并且给出了共变完全多正线性映射的KS- GNS(Kasparov,Stinespring,Gel’fand,Naimark,Segal)构造. 相似文献